1. Выполните действия: a) \(\frac{12}{13} + \frac{4}{13}\) b) \(\frac{5}{6} + \frac{7}{11} + \frac{1}{9}\) c) \(6 \frac{5}{17} - 4 \frac{11}{17}\) d) \(7 - \frac{5}{9}\)

Решение:

a) \(\frac{12}{13} + \frac{4}{13} = \frac{12+4}{13} = \frac{16}{13} = 1 \frac{3}{13}\)

б) \(\frac{5}{6} + \frac{7}{11} + \frac{1}{9} = \frac{5 \cdot 33}{6 \cdot 33} + \frac{7 \cdot 18}{11 \cdot 18} + \frac{1 \cdot 22}{9 \cdot 22} = \frac{165}{198} + \frac{126}{198} + \frac{22}{198} = \frac{165 + 126 + 22}{198} = \frac{313}{198} = 1 \frac{115}{198}\)

в) \(6 \frac{5}{17} - 4 \frac{11}{17} = 6 \frac{5}{17} - 4 \frac{11}{17} = 5 \frac{22}{17} - 4 \frac{11}{17} = (5-4) + (\frac{22}{17} - \frac{11}{17}) = 1 + \frac{22-11}{17} = 1 \frac{11}{17}\)

г) \(7 - \frac{5}{9} = \frac{7 \cdot 9}{9} - \frac{5}{9} = \frac{63}{9} - \frac{5}{9} = \frac{63-5}{9} = \frac{58}{9} = 6 \frac{4}{9}\)